|
%I #33 Jan 15 2020 00:53:05
%S 2,17,80,323,1214,4373,15308,52487,177146,590489,1948616,6377291,
%T 20726198,66961565,215233604,688747535,2195382770,6973568801,
%U 22082967872,69735688019,219667417262,690383311397,2165293113020
%N a(n) = n*3^n - 1.
%H Harry J. Smith, <a href="/A060352/b060352.txt">Table of n, a(n) for n = 1..200</a>
%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>
%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>
%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].
%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,9).
%F G.f.: x*(2-3*x)*(1+3*x)/((1-x)*(1-3*x)^2). - _Colin Barker_, Apr 22 2012
%F a(n) = 7*a(n-1) - 15*a(n-2) + 9*a(n-3), a(1)=2, a(2)=17, a(3)=80. - _Harvey P. Dale_, Dec 14 2012
%F E.g.f.: 1 + exp(x)*(3*exp(2*x)*x - 1). - _Stefano Spezia_, Jan 05 2020
%t Table[n*3^n-1,{n,50}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%t LinearRecurrence[{7,-15,9},{2,17,80},50] (* _Harvey P. Dale_, Dec 14 2012 *)
%o (PARI) { for (n=1, 200, write("b060352.txt", n, " ", n*3^n - 1); ) } \\ _Harry J. Smith_, Jul 04 2009
%Y Cf. A060353.
%K nonn,easy
%O 1,1
%A _Jason Earls_, Mar 31 2001
|
